CFIT; A CE550 CHARTER CREW ALLOWS THE ACFT TO DSND PREMATURELY WHILE ON THE VOR DME APCH TO ASE; CO.

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THE ASPEN APCH CTLR CLRED US FOR THE VOR/DME TO THE ASPEN-PITKEN COUNTY/SARDY FIELD ARPT. THE CTLR VECTORED US TO THE RED TABLE (DBL) VOR AND CLRED US FOR THE APCH (PRIOR TO BEING CLRED FOR THE APCH WE WERE CLRED TO 14000 FT). AFTER BEING CLRED FOR THE APCH WE WERE HANDED OFF TO ASE TWR AND THEN WE BEGAN OUR DSCNT AT DBL TO 12700 FT. AT 3 DME; WE CONTINUED TO 12200 FT AS PUBLISHED. TWR CALLED OPPOSITE DIRECTION TFC. I WENT OUTSIDE TO LOOK FOR THE TFC WHICH WE NEVER HAD A VISUAL ON. WHEN I LOOKED BACK INSIDE; THE PF WAS AT 10800 FT AT 5 DME. I CHALLENGED HIM TO CLB. HE LEVELED; HOWEVER; AND SAID 'DON'T WORRY ABOUT IT; I KNOW WHAT I'M DOING.' AT THE SAME TIME ASE TWR ADVISED THEY HAD AN ALT ALERT WARNING AND HAD US VERIFY WE WERE AT 10800 FT. I VERIFIED IT. AT 6 DME WE CONTINUED TO DSND TO 10400 FT; AT WHICH TIME WE GAINED VISUAL CONTACT WITH THE ARPT. WE WERE THEN CLRED FOR THE VISUAL APCH AFTER STATING SUCH. THE WX AT THE TIME WAS 4000 FT SCATTERED AND 10 MI WITH LIGHT RAIN; WHICH WAS ONE FACTOR. TFC BEING ANNOUNCED AND LOOKED FOR WAS ANOTHER. WE ARE; HOWEVER; WORKING ON OUR CRM SKILLS TO COMMUNICATE; WHICH BROKE DOWN DURING THE APCH.